Question: If $m \angle LON = 180^\circ$ and $m \angle MON = 105^\circ$, what is $m \angle LOM$, in degrees? $105^\circ$ $O$ $L$ $N$ $M$
Answer: From the diagram, we see that $\angle LOM$ and $\angle MON$ are supplementary angles. Therefore, $m \angle LOM + m \angle MON = 180^\circ$ Thus, $m \angle LOM = 180^\circ - m \angle MON = 180^\circ - 105^\circ = 75^\circ$.